They are free to with their own company as they choose. The First Amendment applies only to the government.
I was looking at David Wood yesterday, and he outlined the difference between a platform and a publisher, albeit in the context of Youtube. FB is not a publisher FWICS; there is a difference, and the First Amendment absolutely does apply.
(dons flame retardant underwear)Shocking but true, the First Amendment is overrated. Why?
Because the actual law of rights in America is Common Law. Recall that the Constitution as ratified in 1788 had no bill of rights. Why? Because the Constitution was not intended to affect any common law rights - and the nature of common law is that it wasnt, isnt, and never will be enumerated comprehensively in any one place.
Common Law is a bunch of court precedents, and court precedents grow organically.
Thus, the Federalists aversion to enumerating a bill of rights. But they had to agree to create one by amendment to the Constitution in order to get it ratified. The Ninth Amendment:
The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people.basically reprises the Federalist argument that enumeration of all rights was a fools errand. What is most clear in the first and second amendments is true of the all eight enumerating rights - they werent there to break new ground, but to mollify apprehension about existing rights being modified. Those eight amendments enumerate the rights which tyrants had historically abused.But those enumerated rights are clearly not designed to compromise any other right(s) by stealth, as the Antifederalists feared. Look at the Second Amendment. It speaks of the RKBA - but doesnt define it. But the (existing) RKBA never included the right to commit assault with a gun. Let alone murder anyone.
Likewise the First Amendment speaks of the freedom of the press - but laws against pornography and libel limited freedom of the press at the time. Which is why Justice Brennans claim (in NY Times v. Sullivan that
". . . libel can claim no talismanic immunity from constitutional limitations. It must be measured by standards that satisfy the First Amendmentis fatuous. The First Amendment did not touch libel or pornography law. You have to actually confront Common Law to really know what the Bill of Rights actually means in any specific case. Certainly WRT 1A and 2A.